This invention is related to the time optimal function generator in the coarse positioning system used in a magnetic disc device to position the magnetic heads over a new recording track from a present recording track. The invention more particularly relates to the servo drive circuit for causing the head positioning transducer to accelerate rapidly away from the old track location to the point at which deceleration must occur to arrive smoothly at the new track location.
It is known generally in physics that the fastest way for an object to travel from point A to point B is to accelerate as rapidly and as continuously as possible at the beginning of the journey until that exact point at which continuous rapid deceleration must occur to bring the object smoothly to a stop at the new location B. This principle is employed generally in magnetic disc systems to achieve the most rapid response time consistent with desirable operating conditions. Among these desirable operating conditions is that the magnetic heads arrive at the new track location smoothly without undershooting or overshooting the new location and having to hunt back and forth to arrive at the exact new location. Generally, most present systems contain servo control loops having what is called a time optimal function generator for deriving the position control signal for the position transducer mechanism to achieve the appropriate result. Thus the present invention falls within a category of such time optimal function generators for controlling magnetic disc systems in coarse address positioning operation.
The magnetic recording head servo position control loop for a disk file normally employs a time optimal function generator in the feedback loop to minimize the random average access time. The function generator modifies the position error signal in an approximate square root fashion which achieves a nearly constant deceleration rate for all length seeks. With the deceleration rate set approximately equal to the acceleration rate, time optimal operation is approached and the random average access time is minimized. In addition the recording heads must approach the desired data track with near critical damping to prevent undershoot or overshoot. This requires that the small signal gain of the function generator equals the value required for critical damping of the coarse servo control loop.
The characteristic required of a system for controlling the positioning transducer to produce good settling characteristics without overshoot or hunting is such that the servo system should be critically damped as the error approaches zero. By analysis it can be determined that for small position differences between present location and desired location this servo loop response should be linear. This is in contrast to the desired response of a time optimal function generator when the position difference is large. When large position differences exist this response should be a square root response to produce optimum controlled deceleration.
The coarse positioning loop is normally a second order servo loop. For small perturbations the loop gains are easily set for critical damping. As the perturbations increase in magnitude, a point is reached where proportional control is lost during deceleration. At this point the position error gain needs to be reduced to maintain proportional deceleration control. If the position error signal is reduced in a square root manner, the load will decelerate at a constant rate for a wide range of input perturbations. FIG. 1 shows a typical prior art second order servo control loop with the function generator in the position error portion of the loop.
Previous function generators consist of circuitry employing diode-transistor-resistor networks biased to conduct at selected voltages or break points to approximate a square root transfer function. This invention relates to an improved function generator circuit where the diode-transistor-resistor network is replaced with an inexpensive analog multiplier and the desired transfer function form of A.sub.i =K.sub.1 e.sub.o +K.sub.2 e.sub.o.sup.2 is achieved. Also the direct current drift problem normally associated with analog multipliers used in square root circuits is eliminated.